U.S. patent number 6,382,789 [Application Number 09/404,556] was granted by the patent office on 2002-05-07 for toric ophthalmic lenses.
This patent grant is currently assigned to Essilor International. Invention is credited to Thierry Baudart, Gilles Le Saux.
United States Patent |
6,382,789 |
Baudart , et al. |
May 7, 2002 |
**Please see images for:
( Certificate of Correction ) ** |
Toric ophthalmic lenses
Abstract
A method is provided for determining, by optimization, an
ophthtalmic lens for a spectacle wearer for whom an astigmatism has
been prescribed, comprising the steps of: selecting a starting lens
and defining a working lens to be equal to the starting lens;
selecting a target lens; modifying the working lens, in order to
minimize, in a plurality of directions of glance and in a reference
frame associated with the eye differences in power between the
working lens and the target lens and differences between
astigmatism prescribed and astigmatism generated by the working
lens. The invention makes it possible to avoid aberrations
introduced, for an astigmatic spectacle wearer, by adding a toric
surface having the prescribed astigmatism, thereby ensuring that
the astigmatism effectively experienced by the wearer is the
prescribed astigmatism.
Inventors: |
Baudart; Thierry (Joinville le
Pont, FR), Le Saux; Gilles (Paris, FR) |
Assignee: |
Essilor International
(Charenton Cedex, FR)
|
Family
ID: |
9530925 |
Appl.
No.: |
09/404,556 |
Filed: |
September 23, 1999 |
Foreign Application Priority Data
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Sep 28, 1998 [FR] |
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98 12109 |
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Current U.S.
Class: |
351/159.75 |
Current CPC
Class: |
G02C
7/025 (20130101); G02C 7/061 (20130101); G02C
7/06 (20130101); G02C 7/028 (20130101) |
Current International
Class: |
G02C
7/02 (20060101); G02C 7/06 (20060101); G02C
007/02 (); G02C 007/06 () |
Field of
Search: |
;351/168,169,170,171,172,159,176,177 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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0 274 179 |
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Jul 1996 |
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EP |
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0 857 993 |
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Aug 1998 |
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EP |
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Primary Examiner: Sugarman; Scott J.
Attorney, Agent or Firm: Fish & Richardson P.C.
Claims
What is claimed is:
1. A method for determining, by optimization, an ophthtalmic lens
for a spectacle wearer for whom an astigmatism has been prescribed,
comprising the steps of:
selecting a starting lens and defining a working lens to be equal
to the starting lens;
selecting a reference lens adapted for a wearer for whom no
astignatism was prescribed;
modifying the working lens, in order to minimize, in a plurality of
directions of glance and in a reference frame associated with the
eye:
a difference in modulus between residual astigmatism of said
working lens and astigmatism of the reference lens;
residual astigmatism being defined as the difference between an
astigmatism prescribed and astigmatism generated by the working
lens in the reference frame associated with the eye, and for each
direction of glance.
2. The method according to claim 1, in which power, astigmatism and
residual astigmatism are calculated by ray tracing.
3. The method according to claim 1, wherein prescribed astigmatism
is represented by expansion (A.sub.3, A.sub.4, A.sub.5) thereof
into Zernike polynomials, and in which in each direction of glance,
the wave surface generated by the working lens is represented by
the (expansion (a'.sub.3, a'.sub.4, a'.sub.5) thereof into Zernike
polynomials, and wherein modulus of residual astigmatism in said
direction of glance is equal to 4(a'.sub.3 +L -A.sub.3 +L ).sup.2
+L +(a'.sub.5 +L -A.sub.5 +L ).sup.2 +L .
4. The method according to claim 1, wherein, in each direction of
glance, a wave surface generated by said working lens is
represented by expansion (a'.sub.3, a'.sub.4, a'.sub.5) thereof
into Zernike polynomials, and wherein power in said direction of
glance is equal to 4a'.sub.4.
5. The method according to claim 1, wherein said ophthalmic lens is
a progressive lens.
6. The method according to claim 1, wherein said ophthalmic lens is
a lens dedicated to near vision.
7. The method according to claim 1, in which an orientation of the
reference frame associated with the eye in a direction of glance
(.alpha., .beta.) is deduced from orientation of the reference
frame in the direction .alpha.=.beta.=0 by means of Listing's
law.
8. The method according to claim 1, wherein the said target lens is
a spherical lens.
9. The method according to claim 1, wherein the said step of
modifying the working lens is iterated in order to cause said
differences to decrease.
10. The method according to claim 1, wherein the step of modifying
the working lens comprises modifying one single surface
thereof.
11. A lens obtained by the method according to claim 1.
12. A lens according to claim 11, the surface of which is toric or
spherical.
13. The method according to claim 2 wherein prescribed astigmatism
is represented by expansion (A.sub.3, A.sub.4, A.sub.5) thereof
into Zernike polynomials, and in which, in each direction of
glance, the wave surface generated by the working lens is
represented by the expansion (a'.sub.3, a'.sub.4, a'.sub.5) thereof
into Zernike polynomials, and wherein amplitude of residual
astigmatism in said direction of glance is equal to 4(a'.sub.3 +L
-A.sub.3 +L ).sup.2 +L +(a'.sub.5 +L -A.sub.5 +L ).sup.2 +L .
14. The method according claim 2 wherein, in each direction of
glance, a wave surface generated by said working lens is
represented by expansion (a'.sub.3, a'.sub.4, a'.sub.5) thereof
into Zernike polynomials, and wherein power in said direction of
glance is equal to 4a'.sub.4.
15. The method according claim 3 wherein, in each direction of
glance, a wave surface generated by said working lens is
represented by expansion (a'.sub.3, a'.sub.4, a'.sub.5) thereof
into Zernike polynomials, and wherein power in said direction of
glance is equal to 4a'.sub.4.
16. The method according claim 13 wherein, in each direction of
glance, a wave surface generated by said working lens is
represented by expansion (a'.sub.3, a'.sub.4, a'.sub.5) thereof
into Zernike polynomials, and wherein power in said direction of
glance is equal to 4a'.sub.4.
17. The method according to claim 1, wherein the step of modifying
is further carried out in order to minimize, in a plurality of
directions of glance and in a reference frame associated with the
eye:
a difference between a power of said working lens and a power of
said reference lens.
18. The method according to claim 1, wherein the step of modifying
is further carried out in order to minimize, in a plurality of
directions of glance and in a reference frame associated with the
eye:
a difference in axis between residual astigmatism of said working
lens and astigmatism of the reference lens.
Description
BACKGROUND OF THE INVENTION
The present invention relates to a method for determining an
individual ophthalmic lens adapted to a wearer for whom an
astigmatism has been prescribed; such lenses are also called toric
ophthalmic lenses; they differ from ophthalmic lenses described as
being spherical, the latter being intended to be worn by persons
with no prescription for astigmatism. The method can be applied
both to single-focus or multifocal lenses.
Multi-focal ophthalmic lenses are well-known; among these
multi-focal lenses one can distinguish lenses known as progressive
lenses, and lenses that are more specifically dedicated to near
vision.
Multi-focal lenses present a particular problem for wearers needing
correction of astigmatism. The astigmatism supplied to the wearer
is the resultant of three components:
local cylinder of the progressive surface, characterised by its
amplitude (or modulus) and its axis;
the prescribed cylinder and its axis;
oblique astigmatism.
Currently, to correct a spectacle wearer suffering from
astigmatism, a lens is provided the front face of which is
optimized in the case of a spherical prescription, and the rear
face of which is a simple torus. Thus, account is not taken of the
deterioration introduced by the torus; at best, one can play on the
oblique astigmatism by adjusting the base value of the front face.
For economic reasons, one cannot multiply the number of basic
values existing already.
Multifocal progressive ophthalmic lenses are now well known. They
are used for correcting longsightedness and allow the spectacle
wearer to view objects over a wide range of distances without
needing to take his glasses off. Such lenses typically comprise a
far vision region, situated at the top of the lens, a near vision
region at the bottom of the lens, the far and near vision regions
being joined by an intermediate region, with a main meridian of
progression passing through the three regions.
French Patent 2,699,294 describes the different elements of such a
progressive multifocal ophthalmic lens in its introductory part,
and mentions the works carried out by the applicant to improve the
comfort of wearers of such lenses. Reference should be made to that
document for more details on these various points.
Applicant has also proposed, for example in U.S. Pat. Nos.
5,270,745 or 5,272,495 to introduce a variation into the meridian,
and notably to place it off-center with respect to a near vision
control point, as a function of power addition and ametropy.
Applicant has also proposed, in order to better satisfy the visual
requirements of presbytic (longsighted) persons and to improve
comfort of progressive multifocal lenses, various improvements
(French Patents 2,683,642, 2,699,294 and 2,704,327).
Lenses also exist that are more specifically dedicated to near
vision; these lenses do not have a far vision region with a defined
reference point like one finds in conventional progressive lenses.
Such lenses are prescribed as a function of the power the wearer
needs for near vision, independently of far vision power. Such a
lens is described in an article in the "Opticien Lunetier" of April
1988, and is sold by the applicant under the Essilor Delta
trademark; this lens is simple to use and just as easy to adapt to
as a progressive lens, and is attractive to the population of
presbytic persons not fitted with progressive lenses. This lens is
also disclosed in French Patent application 2,588,973. It has a
central portion which is equivalent to a single-focus lens which
one would normally employ for correcting longsightedness, in order
to ensure satisfactory near vision. It additionally has a slight
decrease in power in the upper portion thereby ensuring the wearer
has sharp vision also beyond the usual field of near vision.
Finally, the lens has a point, at a value of power equal to the
nominal power for near vision, a region of greater power in the
lower portion of the lens, and a region of lower power in the upper
portion of the lens.
Usually, multifocal lenses, whether they be progressive or
dedicated to near vision, have one non-spherical multifocal face,
for example the side facing the spectacle wearer, and one spherical
or toric face, known as the prescription face. This spherical or
toric face allows the lens to be adapted to the users's ametropy,
so that a multifocal lens is generally only defined by its
non-spherical surface. As is well known, such a non-spherical
surface is generally defined by the altitude of all its points. One
also uses parameters constituted by the maximum and minimal
curvatures at each point, or more frequently, their half-sum and
difference. This half-sum and difference multiplied by a factor
n-1, n being the refractive index of the material of the lens, are
known as mean sphere and cylinder.
For progressive multifocal lenses, one thus defines, by choosing a
(power addition, base) pair, a set of non-spherical multifocal
faces. Usually, one can thus define 5 basic values and 12 power
addition values, giving a total of 60 multifocal faces. In each
basic value, an optimization is performed for a given power, i.e.
for a spherical prescription face having a given curvature.
The use within one of these multifocal faces of a spherical or
toric prescription face having a power close to the prescription
face considered for optimization makes it possible to meet all the
requirements of wearers of progressive multifocal lenses. This
known method makes it possible, starting from semi-finished lenses,
of which only the multifocal face has been shaped, to prepare
lenses that are adapted to each wearer, by simply machining one
spherical or toric prescription face.
A similar method is used for optimization and prescription of
lenses dedicated to near vision.
This method has the disadvantage of only being an approximation;
consequently, the results obtained with a prescription face that is
different from that used for optimization are worse than those
corresponding to the prescription face employed for
optimization.
U.S. Pat. No. 5,444,503 discloses a lens having a multifocal
surface and a prescription surface. Compared to the prior art,
which suggests defining the prescription service in order to obtain
a given power at the far vision reference point, it is proposed, in
that Patent, to define the prescription surface of the lens as a
function of the power required by the wearer in a plurality of
elementary surfaces. For this, the said United States.
Patent involves calculating aberration over the whole surface, and
causing a continuous parametered surface to vary, for example a
surface defined by splines, using known mathematical optimization
algorithms. In practice, beyond the statement of principle, that
Patent proposes using, in order to optimize the prescription
surface, the distance to the cornea in an elementary surface, the
object distance in an elementary surface, the inclination of the
lens in the frame, the shape of the frame, and the curvature of the
lens. That Patent says nothing regarding the effective calculation
of the prescription surface. According to that document, their
solution would make it possible to overcome the defects originating
from replacement of the rear face used for optimization, by a rear
face close to it.
That solution has the disadvantage of complicating lens
manufacture: it involves determining, and machining, a
non-spherical rear face. In this case, one should optimise and
machine two complex surfaces. The proposed method does not appear
to be founded on physiological data.
International application WO-A-96/13748 further discloses the use,
for multifocal lenses, of a non-toric prescription surface, in
order to limit defects with respect to the prescription surface
employed for optimization. That Patent discloses prescription
surfaces the main cross sections of which are circles having a
radius defined by a given equation, the parameters of the equation
depending on the wearer's sphere and cylinder. The solution
disclosed in that document suffers from the same disadvantages as
those described with reference to U.S. Pat. No. 5,444,503.
International application WO-A-97/19382 discloses a progressive
ophthalmic lens having a front face that is spherical or exhibits
symmetry of revolution, and a rear face obtained by combining a
progressive surface having a power addition and a toric surface in
which the torus is adapted to the wearer's astigmatism. The formula
for combining these two surfaces is stated in the Patent, and gives
the altitude of a point as a function of its coordinates in an
orthonormalized reference frame, of mean sphere of the progressive
surface at this point, and of curves for the progressive surface in
the directions of the orthonormalized reference frame.
The algebraic combination of the two surfaces in that patent, using
the given formula for combination, does not give satisfactory
optical results. This method obliges the manufacturer to re-incline
the front surface of the lens to obtain a satisfactory optical
quality, thereby deteriorating lens aesthetics.
The prior art Patents say little or are not explicit regarding
calculation techniques. Their techniques do not appear to be
founded on physiological data, and do not use ray tracing.
SUMMARY OF THE INVENTION
The invention provides a method for determining a toric lens, based
on a physiological law, making it possible to take account of the
torsion of the eye for any given direction of glance. For each
direction of glance, it is arranged for power and astigmatism, both
as regards their value and direction, to be as close as possible to
the prescription in the reference frame associated with the eye.
Calculation of astigmatism in this reference frame makes it
possible to take account of the effect of torsion of the eye, when
the spectacle wearer is looking in an off-center direction. The
method employs ray tracing and consequently an optical method.
The invention discloses a method making it possible to define a
lens adapted for a toric prescription, the target being the
behavior of a spherical lens; in this context, we shall call a
spherical lens a lens that is adapted to be prescribed for a
non-astigmatic wearer; i.e. not having overall cylinder.
The invention thus makes it possible to obtain lenses that are
suitable for astigmatic spectacle wearers, which have better
optical characteristics than those of the prior art.
The general method disclosed, which can be applied to any type of
lens, makes it possible to overcome the disadvantages due to torus
in a conventional toric prescription, and to give the spectacle
wearer a perception which is equivalent to that of a spherical
prescription.
The invention also provides for calculation of a lens that is
unique for each prescription. Using other parameters, such as the
shape of the frame, the distance between the cornea and the lens,
the pantoscopic angle, it is possible to calculate a lens for each
wearer.
More precisely, the invention discloses a method for the
determination, using optimization, of an ophthtalmic lens for a
wearer for whom an astigmatism has been prescribed, comprising the
steps of:
selecting a starting lens and defining a working lens to be equal
to the starting lens; selecting a target lens;
modifying the working lens, in order to minimize, in a plurality of
directions of glance and in a reference frame associated with the
eye:
a difference between power of said working lens and power of the
said target lens;
a difference between residual astigmatism and astigmatism of the
target lens;
residual astigmatism being defined as the difference between an
astigmatism prescribed and astigmatism generated by the working
lens both as regards amplitude and the axis thereof in the
reference frame associated with the eye, and for each direction of
glance.
Advantageously, power, astigmatism and residual astigmatism are
calculated by ray tracing.
In a preferred embodiment, prescribed astigmatism is represented by
expansion (A.sub.3, A.sub.4, A.sub.5) thereof into Zernike
polynomials, and in which, in each direction of glance, the wave
surface generated by the working lens is represented by the
expansion (a'.sub.3, a'.sub.4,a'.sub.5) thereof into Zernike
polynomials, and wherein amplitude of residual astigmatism in said
direction of glance is equal to
In another embodiment, in each direction of glance, a wave surface
generated by said working lens is represented by expansion
(a'.sub.3, a'.sub.4, a'.sub.5) thereof into Zernike polynomials,
and power in said direction of glance is equal to 4a'.sub.4.
Preferably, the ophthalmic lens is a progressive lens.
In one embodiment, the ophthalmic lens is a lens dedicated to near
vision.
Advantageously, orientation of the reference frame associated with
the eye in a direction of glance (.alpha., .beta.) is deduced from
orientation of the reference frame in the direction (a'.sub.3,
a'.sub.4, a'.sub.5).alpha.=.beta.=0 by means of Listing's law.
Preferably, the said target lens is a spherical lens.
In one embodiment, the step of modifying the working lens is
iterated in order to cause said differences to decrease.
In another embodiment, the step of modifying the working lens
comprises modifying one single surface thereof.
A lens obtained by the above method, the surface of which is toric
or spherical, is also provided.
Other advantages and characteristics of the invention will become
more clear from the description which follows of several
embodiments, provided by way of example and with reference to the
attached drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows an eye and lens optical system.
FIGS. 2 and 3 are diagrams defining a reference frame associated
with the eye.
FIGS. 4-7 show the optical characteristics of a prior art lens.
FIGS. 8-10 show the optical characteristics of a reference
lens.
FIGS. 11-14 show the optical characteristics of the lens the front
face of which is optimized according to the invention, and for a
rear face that is substantially different from that of the prior
art lens.
FIGS. 15-17 show the surface characteristics of the front face of a
lens optimized according to the invention.
FIGS. 18-20 show surface characteristics of the rear face of a
starting lens, in a second embodiment of the invention.
FIGS. 21-23 show the optical characteristics of a reference
lens.
FIGS. 24-27 show the optical characteristics of a lens the rear
face of which is optimized according to the invention.
FIGS. 28-30 show the surface characteristics of the rear face of
the lens optimized according to the invention.
FIGS. 31 to 34 show the optical characteristics of a lens similar
to the prior art.
FIGS. 35-38 show the optical characteristics of a single-focus lens
the front face of which is optimized according to a third
embodiment of the invention.
FIGS. 39-41 show the surface characteristics of the front face of
the optimized single-focus lens.
FIGS. 42-45 show the optical characteristics of a lens similar to
the prior art.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
As is known per se, a mean sphere D can be defined for every point
on a non-spherical surface, given by: ##EQU1##
where R1 and R2 are maximum and minimum radii of curvature
expressed in meters, and n is the refractive index of the material
from which the lens is made.
A cylinder is also defined, given by: ##EQU2##
For a given lens, for example a multifocal lens, the corresponding
optical values are defined, specifically power and astigmatism; the
power is defined as explained below. Astigmatism is calculated for
example as described in B. Bourdoncle et al, "Ray tracing through
progressive ophthalmic lenses", 1990, International Lens Design
Conference, D. T. Moore ed., Proc. Soc. Photo. Opt. Instrum. Eng.
One thus obtains possible definitions of the optical power and
astigmatism of the lens, under the conditions in which it is worn.
By the conditions under which a lens is worn, we mean the position
of the lens with respect to the eye of an average spectacle wearer,
notably defined by the pantoscopic angle, which is around
12.degree., by the distance between the lens and the eye, and the
distance between the pupils.
One can not only use these definitions, but also determine power
and astigmatism from coefficients resulting from decomposition of
the wave surface. One further obtains definitions representative of
wearing conditions.
FIG. 1 is a diagram of an eye and lens optical system, showing the
definitions employed in the remainder of this specification. Q' is
the center of rotation of the eye, and a sphere of the vertices,
centered on Q', is defined having a radius q', which is tangential
to the rear face of the lens at a point in the horizontal axis. For
example, a value for the radius q' of 27 mm corresponds to a common
value and gives satisfactory results when the lenses are worn.
A given direction of glance corresponds to a point J on the sphere
of vertices, and can also be defined, using spherical co-ordinates,
by two angles .alpha. and .beta.. Angle .alpha. is the angle formed
between the straight line Q'J and the horizontal plane passing
through the point Q', while angle .beta. is the angle formed
between straight line Q' J and the vertical plane passing through
the point Q'. A given direction of glance thus corresponds to a
point J on the sphere of vertices or to a pair (.alpha., .beta.).
The image of the points in the object space, and in a direction of
glance, and at a given object distance, is formed between two
points S and T corresponding to a minimum and maximum focal length,
which would be the sagittal and tangential focal lengths in the
case of surfaces of revolution. On the optical axis, the image of a
point in the object space at infinity is formed at point F'. The
distance D is the focal length of the eye-lens system.
The term ergorama will be used to describe a function which maps
each direction of glance to the distance of the object point
habitually viewed; for more details of a possible definition of an
ergorama, reference can be made to French Patent 2,753,805, which
describes an ergorama, its definition and modelling process. A
particular ergorama consists in only adopting points at infinity.
For the method of this invention, points that are at infinity or
not at infinity can be considered.
FIG. 2 shows the position of the eye and of the reference frame
associated with the eye, in the main direction of glance,
.alpha.=.beta.=0, known as the primary direction of glance. FIG. 3
shows the position of the eye and the reference frame associated
therewith in a direction (.alpha., .beta.).
Let {x, y, z} be a fixed reference plane centered on Q'; axes x
passes through the lens center, the y axis is the vertical, and the
z axis is the horizontal. A reference frame associated with the eye
is identified by {x.sub.m, y.sub.m Z.sub.m }, centered on Q', the
axis xm of which is given by the direction of glance, and which
coincides with reference frame {x, y, z} for the primary direction
of glance. Listing's law gives the relations between the reference
frames {x, y, z} and {x.sub.m, y.sub.m, z.sub.m } see Legrand,
"Optique physiologique" vol. 1, published by the Revue de
l'optique, Paris 1969.
It is now possible to define, within the reference frame associated
with the eye, and in a given direction of glance, the orientation
and value of astigmatism as well as the power value, from a
decomposition of the wave surface entering the pupil of the eye,
which, for the sake of simplicity, we shall suppose has unit
radius; these values correspond to the value and orientation of the
astigmatism as well as the power which is effectively perceived by
the wearer. The wave surface entering the pupil of the eye in each
direction of glance can be obtained in a known manner by ray
tracing.
In a manner known per se, a wave surface can be decomposed, on a
unit radius pupil, using Zernike polynomials; in the ophthtalmic
field, one generally limits oneself to the initial terms of this
representation. A wave surface can be approximated by a linear
combination of polynomials, of the type: ##EQU3##
in which p.sub.i are the Zernike polynomials, and a.sub.i are the
real coefficients. For each direction of glance, the wave surface
entering the pupil of the eye can be consequently expressed by the
following relations, in which p.sub.i are the Zernike polynomials
mapped to the reference frame associated with the eye:
##EQU4##
The invention carries out this expansion into polynomials in a
reference frame associated with the eye, for example, the reference
frame {xm, ym, zm} mentioned above. In this case, the coefficients
a3, a4 and a5 are representative of mean power and of astigmatism
through the following relations:
the variable term in mean power is now given by 4a.sub.4,
the modulus of astigmatism is given by 4a.sub.3.sup.2 +L
+a.sub.5.sup.2 +L , and
the axis of astigmatism is obtained from the ratio a3/a5.
Other definitions of power or astigmatism in a reference frame
associated with the eye could be employed, taking account of other
coefficients of the decomposition, but the ones we employ have the
advantage of being simple and of being able to be calculated
readily using a ray tracing program, for a given lens.
The invention further employs this wave surface modelling in each
direction of glance for the definition of an ophthtalmic lens,
taking account of the wearer's physiological data.
For this, we consider the prescription the wearer needs for far
vision, as regards power and astigmatism, which can be transformed
into coefficients (A.sub.3, A.sub.4, A.sub.5). These coefficients
are descriptive of the wave surface it is necessary to generate in
order to perfectly correct the wearer's far vision. Expressing this
in the Listing reference frame associated with the eye, the set of
these three coefficients remains constant for all directions of
glance.
Next, we consider a reference lens, which is a spherical lens, i.e.
having no torus or astigmatism; we can take as a reference lens, a
lens having a power addition and a mean power that are identical to
those that were prescribed; one solution in the case of a
progressive multifocal lens consists in considering the applicant's
spherical lens of the type disclosed in French Patent applications
2,683,642, 2,683,643 and 2,699,294 and which are marketed under the
Varilux trademark.
To this reference lens, there corresponds, in each direction of
glance, a wave surface for a given object space and for given lens
mounting conditions; one can thus derive from this a set of three
coefficients (A.sub.3, A.sub.4, A.sub.5) for each direction of
glance. For the given object space, we can consider the ergorama of
the type mentioned above, or any object space whatsoever. As
regards mounting, we can consider conventional mounting conditions
such as those described in the applicants above Patent application;
we could also consider the mounting conditions for a given
wearer.
One can, from these various sets of coefficients (a.sub.3, a.sub.4,
a.sub.5) and from the prescription (A.sub.3, A.sub.4, A.sub.5)
define, for each direction of glance, a target wave surface,
suitable for use for optimizing a lens. In each direction of
glance, the target wave surface is represented by a set of three
coefficients (a'.sub.3, a'.sub.4, a'.sub.5), with
The first relations (1) expresses the fact that it is desired to
preserve the power behavior of the reference lens.
The second relation represents "residual" astigmatism,
corresponding to the difference between the astigmatism created by
the lens and the astigmatism prescribed for the wearer; this
reflects the fact that the presence of the torus should not impair
the performance of the reference lens. It will be noted that the
invention is here described on the assumption that the prescribed
astigmatism for far vision is in fact the astigmatism to be applied
in each direction of glance, in the eye's reference frame. One
could just as well adapt values of astigmatism and change the set
of coefficients (A.sub.3, A.sub.4, A.sub.5) as a function of the
various directions of glance.
A constraint applying to residual astigmatism is that it must be
equal to the reference lens's astigmatism; in the ideal case,
residual astigmatism should be zero in each direction of glance. It
has proved that this ideal constraint does not always make it
possible to obtain a physical solution; the constraint imposed by
the relation (2) is less rigorous than the ideal constraint, and
does make it possible to obtain a solution. The choice of the
proposed reference lens ensures that, in the foveal regions,
astigmatism is substantially zero, and thus:
implying
a'.sub.3 =A3 and
a'.sub.5 =A.sub.5
Because of this, the axis of the astigmatism and its modulus are
equal to the axis of the prescribed astigmatism and its modulus, at
least in the foveal region.
These two relations do in fact define a target lens, which can be
employed for lens optimization in an optimization program, as
explained below. This target lens:
has the behavior and power of the reference lens;
has residual astigmatism equal to the astigmatism of the reference
lens.
In the example given above, the reference lens has the same power
and the same power addition as the lens prescribed. One could just
as well choose as the reference lens a lens having a power or power
addition different from that prescribed. In this case, relation (1)
would be written as:
in which m and n are two real values chosen so that the far vision
power and the power addition have the prescribed values. In other
words, m and n are solutions to two equations having two unknowns,
in the directions of glance for which the prescription is known,
i.e. for far and near vision.
The invention proposes using these target values for defining
lenses, using an optimization method which is known per se. It will
be noted that the invention has been described above for the most
complex case where the lens is a progressive multifocal lens; it
applies just as well to optimization of spherical lenses, which
correspond to a particular case where
The invention also applies to the case of a single-focus lens,
which corresponds to
Finally, the invention advantageously uses a ray tracing program
for determining the optimized surface, under physiological
conditions; it makes it possible to optimise a front face of the
lens, for a given rear face, or vice-versa.
We shall now describe a method for optimization which can be
employed for carrying out the invention. The aim of the
optimization process, setting out from a starting lens, is to cause
the parameters defining at least one of the surfaces of a working
lens to vary in order to satisfy as closely as possible,
constraints (1) and (2) defined above.
For this, we can consider a merit function representing the
differences between the lens to be optimized and the target lens,
defined as follows. For a set of points on the lens, or a set of
glance directions, referenced by a variable i, we shall consider
the merit function written in the form: ##EQU5##
Where p.sub.i is a weighting for point i;
V.sub.ij is the value either of residual astigmatism, or of the
power at point i, for the working lens;
C.sub.ij is the value either of target astigmatism, or of target
power;
w.sub.ij is the weighting for the difference in astigmatism'or
power at point i.
We thus define in this way a target, and a merit function which is
representative of the difference in optical characteristics between
a lens and the said target. Such a merit function is obviously
positive and it should be minimised during the optimization
process.
In order to proceed with optimization, it is now sufficient to
select a starting lens and a method of calculation which makes it
possible to decrease, through iteration, the value of the merit
function. For this, one can advantageously employ a damped least
squares method, or yet again any other optimization method known
per se. By using a damped least squares method and a merit function
of the type defined above, ten or so iterations are sufficient to
yield, in the majority of cases, a lens having good
performance.
In order to proceed with optimization, one can advantageously use,
for the lens to be optimised, a decomposition of the wave surface
at the pupil of the eye, using Zernike polynomials, in order to be
able to directly employ constraints in the form of relations (1)
and (2) given above. In this case, one can set out from the
starting lens and add a layer to be optimized to the corresponding
surface, and then only modify this layer in the optimization
process, this layer itself being able to be modeled by means of
Zernike polynomials.
We shall now give examples of optimization using such expansion
into Zernike polynomials. The prescription, as indicated above,
provides a set of three coefficients (A.sub.3, A.sub.4, A.sub.5);
the reference lens supplies, in directions of glance corresponding
to the points i selected, the sets of three coefficients (a.sub.3,
a.sub.4, a.sub.5).sub.i.
The target is written now, in each direction of glance or for each
point i as:
for the corresponding set of coefficients (a.sub.3, a.sub.4,
a.sub.5).
The working lens has, in the direction of glance corresponding to
point i, a current power value of
and for V.sub.i2, residual astigmatism, as explained above, we
use:
The values of a'3, a'4 and a'5 are now varied at various points i,
in order to decrease the merit function, as explained above.
At the end of optimization, an altitude map of the optimized
surface, defining the surface to be provided, is obtained.
The examples that follow give several embodiments of the
invention.
EXAMPLE 1
In this example, we optimise the front surface of a lens the rear
surface of which is a toric surface of the type used in the prior
art, but which does not necessarily correspond to the toric
prescription for the spectacle wearer. We attempt to obtain a
multifocal lens for the following prescription:
far vision power: 3 diopters;
astigmatism: 2 diopters;
axis of astigmatism: 135.degree.;
addition: 2 diopters;
refractive index: 1.502.
FIGS. 4 to 7 show the optical characteristics of a prior art lens;
FIG. 4 shows power along the meridian, with the definition of power
as given above. The x-axes are graduated in diopters, and the
y-axes give the height, in degrees, on the lens; the solid line
indicates power and the dashed lines the amounts 1/JT and 1/JS
defined in FIG. 1, for object distances corresponding to an
ergorama representative of the distances of object points in each
direction of glance, in order to ensure optimum comfort for the
wearer. FIG. 5 shows lines of equal power, i.e. lines formed by
points for which power has an identical value. The x-axis and
y-axis respectively give the angles .beta. and .alpha.. FIG. 6
shows, using the same axes, lines of equal oblique astigmatism.
FIG. 7 shows residual astigmatism, as defined above.
This lens is a prior art lens, in which the rear face carries the
torus, while the front face is a multifocal progressive surface
such as those disclosed in the applicant's Patents. This lens has a
base of 6.20 diopters, a far vision power of 2.97 diopters, a power
addition of 1.97 diopters and an astigmatism of 2.11 diopters, with
an axis of 135.degree..
FIGS. 8 to 10 show optical characteristics of the reference lens
employed for optimization; this lens is a spherical lens, having
the same power equal to 2.97 diopters for far vision, the same
power addition equal to 1.98 diopters, and no astigmatism. FIGS. 8
to 10 are produced similarly to FIGS. 4 to 6, using the same
conventions.
FIGS. 4 to 11 show the optical characteristics of the lens
optimized according to the invention; FIGS. 4 to 11 have also been
produced similarly to FIGS. 4-7, using the same conventions. As
indicated above, it is the front face that has been optimized,
using a starting lens having the same front face as the prior art
lens, but with an approximated toric rear face, and the lens in
FIGS. 8 to 10 as a reference lens. The Figures show that the
optical characteristics of the lens optimized according to the
invention are very close to those of the reference lens. We have
thus avoided the aberrations introduced by the toric rear face of
the prior art lens. The lens has a base value of 6.63 diopters, a
far vision power of 3.02 diopters, a power addition of 1.94
diopters and an astigmatism of 1.99 diopters on an axis of
135.degree..
FIGS. 15 to 17 show surface characteristics of the front face of
the lens in FIGS. 11-14. FIG. 15 shows surface power or mean sphere
D, as defined above: the solid line shows mean sphere, and the
dashed lines the values C.sub.1 =(n-1)/R.sub.1 and C.sub.2
=(n-1)/R.sub.2 with R1 and R2 being the principal radii of
curvature. The x-axis is graduated in diopters and the y-axis gives
the height on the front face, in millimeters. Mean sphere at the
far vision reference point is 6.63 diopters for a cylinder of 0.63
diopters; mean sphere at the near vision reference point is 8.63
diopters, for a cylinder of 0.64 diopters. It will be noted from
this representation alone that the invention leads to cylinder or
torus being distributed over both faces of the optimized lens.
FIG. 16 shows lines of mean isosphere for the front face of the
lens; the axes are graduated in millimeters; FIG. 17 shows
isocylinder lines, using the same axes. These Figures show that the
front face of the lens of the invention is very different from the
front faces of conventional lenses.
The invention, as implemented in this example, shows the
aberrations introduced by prior art methods, and shows how the
invention, by taking account of the spectacle wearer's
physiological data, and thanks to optical calculations, makes it
possible to reduce these aberrations. We thus correct the
aberrations introduced by the torus in the prior art lens, and we
provide the spectacle wearer with foveal vision that is equivalent
to that of an emmetropic spectacle wearer with the same power
addition. We also show that the toric part missing in the starting
lens is transferred to the front face.
EXAMPLE 2
In this example, the invention is applied to the optimization of
the rear face of a progressive multifocal lens, for which torus and
degression are situated on the rear face of the lens.
The prescription is as follows:
far vision power: 3 diopters;
astigmatism: 2 diopters;
axis of astigmatism: 45.degree.;
power addition: 2 diopters;
refractive index: 1.502 diopters.
The front face of the lens is spherical.
FIGS. 18-20 show, using the same conventions as those of FIGS.
15-17, surface characteristics of the rear face of the starting
lens; the front face is spherical; the rear face is calculated in
an approximate manner by summing the altitudes of a conventional
multifocal progressive surface and a toric surface, taking account
of the front face. More precisely, the following three surfaces are
considered:
S 1: progressive surface of power addition 2.00 diopters, and base
6.20 diopters;
S 2: sphere of radius identical to the radius for far vision of the
conventional progressive surface;
S 3: toric surface providing an astigmatism of 2.00 diopters and a
power of 3.00 diopters for the front face considered.
The altitude of a point on the rear starting face is given by
where z.sub.1,z.sub.2 and z.sub.3 are the respective altitudes of
the three surfaces S.sub.1, S.sub.2 and S.sub.3 ; the terms
-z.sub.1 +z.sub.2 approximately define a plane surface for far
vision and a surface that is degressive for near vision; the term
z.sub.3 adds the expected toric effect. In this way, we obtained a
rear face of a mean sphere for far vision equal to 3.34 diopters,
of degression 2.18 diopters. At the far vision reference point, the
rear face has a cylinder of 1.99 diopters, and at the near vision
reference point, it has a cylinder of 2.07 diopters. The front face
of the lens has a spherical surface of radius 6.20 diopters.
FIGS. 21-23 show, using the same conventions as FIGS. 8-10, optical
characteristics of the reference lens. For the reference lens, we
have used a lens having a conventional progressive front face and a
spherical rear face; the lens has zero power for far vision, a
power addition of 2.19 diopters, and a base of 6.20 diopters as
indicated above.
FIGS. 24-27 show optical characteristics of the lens optimized
according to the invention, using the same conventions as in FIGS.
11-14. The optimized lens has a power at the far vision reference
point of 2.98 dioptes, an astigmatism at the same point of 1.94
diopters, a power at the near vision reference point of 5.12
diopters, and an astigmatism at the same point of 1.97 diopters.
This lens is obtained by adding a power of 3 diopters to the
reference lens employed.
FIGS. 28-30 show surface characteristics of the rear face of the
lens optimized ccording to the invention, using the same
conventions as in FIGS. 15-17. The rear face has a mean sphere of
3.34 diopters at the far vision control point and a cylinder of
1.79 diopters. At the near vision reference point, the rear face
has a mean sphere of 1.49 diopters, and a cylinder of 1.59
diopters. Degression of the rear face is 1.85 diopters.
FIGS. 31-34 show, for the purposes of comparison, the optical
characteristics of a prior art lens. The conventions used are the
same as those in FIGS. 24-27. Again it will be noted, as in the
example of FIG. 11, that the lens optimized according to the
invention has smaller aberrations than those of the prior art lens.
Additionally, residual astigmatism, as experienced by the spectacle
wearer, is close to the astigmatism of the reference lens.
EXAMPLE 3
In this example, the front surface of a single-focus lens was
optimized, the rear face of which included a conventional
torus.
The prescription is as follows:
sphere: 0 diopters;
cylinder: 2.75
axis of cylinder: 90.degree.;
refractive index: 1.604.
The starting lens had a spherical front face with a base equal to
4.58 diopters. The rear face corresponded to the prescription
according to the prior art.
In this very simple case, the targets for resultant astigmatism are
assumed to be zero and the targets for power are all identical and
equal to 1.375 diopters.
FIGS. 35 to 38 show, using the same conventions as in FIGS. of 4-7,
the optical characteristics of the lens optimized according to the
invention. At the control point, power is 1.39 diopters, and
astigmatism is 2.74 diopters.
FIGS. 39-41 show, using the same conventions as in FIGS. 28 to 30,
surface characteristics of the front face of the optimized single
focus lens. Mean sphere at the control point is 4.58 diopters, and
cylinder is 0.02 diopters.
By way of comparison, FIGS. 42-45 show the optical characteristics
of a non-spherical lens of the prior art for the same prescription.
The same conventions have been used as in FIGS. 35 to 38.
It will again be noticed that the invention makes it possible to
reduce aberration and to obtain a lens for which residual
astigmatism as experienced by the spectacle wearer, is
substantially zero.
The invention makes it possible, for multifocal or single focus
lenses, to obtain optical characteristics similar to those of the
best lenses of the prior art, and this despite a prescription for
astigmatism. The method of the invention provides results better
than the solution proposed in WO-A-97/19382: indeed, it makes it
possible to take account of the optical properties of the lens as
effectively experienced by the wearer, and not only algebraic
calculation which of necessity is approximate.
It is clear that in all these examples, one can readily reverse the
role of the front and rear surfaces. One can also distribute power,
torus and progression at will over one or the other of the two lens
surfaces, or partly on one surface and partly on the other. In the
case of progressive lenses, a plane lens having the same power
addition can be used as a target, as in example 1; one can just as
well use a progressive lens having a power equivalent to the power
prescribed.
Obviously, it is possible to employ other methods of optimization,
and other ways of representing surfaces differing from the method
proposed and the representations in terms of wave surfaces
decomposed into Zernike polynomials.
* * * * *